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Number field normalization #25

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fredrik-johansson opened this issue May 4, 2021 · 0 comments
Open

Number field normalization #25

fredrik-johansson opened this issue May 4, 2021 · 0 comments

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@fredrik-johansson
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ca_set_qqbar should try harder to standardize:

  • Maybe sqrt(-3) -> exp(2 pi / 3) and sqrt(5) -> phi, etc. (like Pari does)
  • For roots of unity, maybe standardize to exp(2 pi i /n)
  • Make a choice when there is real/imaginary symmetry
  • Always normalize to a monic polynomial
  • After normalizing to a monic polynomial, use some more heuristics; at least try to find a linear transformation that minimizes content
  • For low-degree polynomials, implement polredabs / polredbest
  • Recognize cyclotomic and trigonometric fields at least in some cases (expensive at high degrees)
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